On Optimal Scale Selections And Rule Extraction In Several Types Of Multi-scale Decision Systems

Building models for multi-scale data among "multi-granularity" environment has become an important direction in granular research.Many generalized rough set models have been developed.A basic model is multi-scale information systems assuming that all attributes have the same scale numbers.The purpose of this dissertation is to investigate the connection among several optimal scales and to extract local rules for a specific set containing a given object.Three main contents are as follows:Using a maximal consistent block technique,Chapter Two is a comparative study of different optimal scale selections in numerical incomplete multi-scale decision systems.Firstly,the concept of scale in this model is introduced.Secondly,several maximal consistent block based optimal scales are defined.Finally,the relationship between them is clarified.For consistent numerical incomplete multi-scale decision systems,a scale is optimal if and only if it is a maximal consistent block based optimal scale.And for inconsistent numerical incomplete multi-scale decision systems,there is no static relationship between a maximal consistent block based lower-approximation optimal scale and an upper-approximation optimal scale.Adopting generalized-decision local optimal scale combinations,Chapter Three is a knowledge acquisition for an object in inconsistent generalized complete multi-scale decision systems.Firstly,the notion of scale combinations in generalized complete multi-scale decision systems is reviewed.And information granules with different scale combinations are formulated.Secondly,the relationships between seven types of local optimal scale combinations are studied.Finally,there are only five different concepts.And based on a generalized-decision local optimal scale combination,attribute reductions and rules for each object can be obtained.Combining the maximal consistent block technique and its local optimal scale combination,Chapter Four is a rule induction in incomplete generalized multi-scale intervalvalued decision systems.Firstly,an incomplete generalized multi-scale interval-valued decision system is defined.Secondly,the notion of maximal consistent block based local optimal scale combination is proposed.Finally,the notion of scale reduct is constructed.It is a type of scale combination that can reflect attribute reduction simultaneously.Relying on its lattice structure,two relevant algorithms are designed to search for optimal scale combinations and attribute reductions synchronously.